Function generator for producing square and ramp wave pulses

ABSTRACT

A rapid process simulator for determining both static and the dynamic characteristics which are unknown in a relatively stable process. The simulator includes a pulse generator for producing a perturbating pulse which is applied to the process. The perturbating pulse produces an output signal which can be expressed in the form of a polynomial. The process is compared in the simulator with a model of orthogonal functions which are capable of being normalized to an orthonormal condition. The model is formulated with the idea of choosing a pulse input in such a way as to facilitate the construction of the system. An output signal is also produced in the model which is in turn compared with the output signal from the process in order to achieve an error signal. This signal is squared in the simulator and integrated to determine the characteristics of the system. The simulator includes a transport delay device for delaying the perturbating pulse to the model with respect to the process, so that the output of the process and the model will begin in coincident times. In addition, the simulator is provided with a generator to produce oscillatory transients on a model of the signal to match transient on the process signal.

United States Patent [72] Inventors Louis ll. Fricke, Jr.

St. Louis; Robert A. Walsh, Richmond Heights, Mo. [21] Appl. No. 870,812[22] Filed Aug. 25, 1969 Division of Ser. No. 495,565, Oct. 13, 1965,Pat. No. 3,505,512.

[45] Patented Apr. 6, 1971 [73] Assignee Monsanto Company St. Louis, Mo.

[54] FUNCTION GENERATOR FOR PRODUCING SQUARE AND RAMP WAVE PULSES 4Claims, 15 Drawing Figs.

[52] US. Cl 235/197, 328/127, 328/36 [51] Int. Cl G06g 7/26 [50] Fieldof Search 235/197,

183,l84;328/180,181,182,183,184,185, 127, 34, 35, 36; 307/(lnquired)Primary Examiner-Malcolm A. Morrison Assistant Examiner.loseph F.Ruggiero AttorneysRobert J. Schapp, Joseph D. Kennedy and John D.

Upharn ABSTRACT: A rapid process simulator for determining both staticand the dynamic characteristics which are unknown in a relatively stableprocess. The simulator includes a pulse generator for producing aperturbating pulse which is applied to the process. The perturbatingpulse produces an output signal which can be expressed in the form of apolynomial. The process is compared in the simulator with a model oforthogonal functions which are capable of being normalized to anorthonormal condition. The model is formulated with the idea of choosinga pulse input in such a way as to facilitate the construction of thesystem. An output signal is also produced in the model which is in turncompared with the output signal from the process in order to achieve anerror signal. This signal is squared in the simulator and integrated todetermine the characteristics of the system. The simulator includes atransport delay device for delaying the perturbating pulse to the modelwith respect to the process, so that the output of the [56] Reterencescued process and the model will begin in coincident times. In addi-UNITED STATES PATENTS tion, the simulator is provided with a generatorto produce 3,255,416 6/1966 Stella 328/36 oscillatory transients on amodel of the signal to match 3,500,445 3/1970 Collings 235/197 transienton the process signal.

r S /P LINE POWER SUPPLY RELAY a PROCESS I} REFERENcE VOLTAGE III ll 23a: T 1 1 1 DlGtTAL QS fig RESET E p p VOLT METER AMPLIFIERS GENERATORCONVERTER CONVERTER PULSE 27 32 I ELECTRICAL ELECTRICAL |3\ GENERATORRANGE RANGE SELECTOR coNvERTER SQUARE 7 a7 e r--- wAvE 22 1 SAMPLER 1/INTE- ADDER I l I fiw "HSQUARER GRATOR s RAMP J REsE-rl H... WAVE lREsETSAMPLER IE *2 I I MODEL 1 5 sea. 3 )-4l WAVE SAMPLER 24 \M I l I 1 PROC.85%} OSCILLATORY WAVE r- TRANSTENTs sAMPLER 30 GENERATOR /T REsETREcoRoER Pmmmd A N 6 WW 9 Sheets-Sheet 1 W m Wm M mA Hm m LR PmmmdlApmrill 6 WW mwmm 9 Sheets-Sheet F'FRMNGTMTL AWWME GEMEFR'M'TO R" I I IFROM I RESET POWER I POWER SUPPLY i H I I a II I I I I POWER FOR 7P3: IAMPLIFIERS K I I l I I LMQRR mwwwmwn F .WENTORS LOUIS H, FRICKE,JR.ROBERT A, WALSH F I63 a1.

ATTORNEY Pmmmmd in H1 9 Sheets-Sheet QLECILLATORY TRANEEENTS GENERATOR ll i l l I l I I L INVENTORS LOUIS H. FRICKEJR. ROBERT A. WALSH c m m FATTORNEY II "M 9 Sheets-Sheet 6 r--'"' AMPLITUDE i/l 1 /DURATION o DELAY2 if AMPLITUDE I? I W ,/I' TRAI\IsPoRT DELAY DURATION SIGNAL AMPLITUDECOMPUTE CYCLE FIGA.

INVENTORS LouIs H FRICKE, JR. ROBERT A. vvALH 613% y. M V

ATTORNEY Pmmm April 6 fi 9 Sheets-Sheet 7 IELEC'TRICAL& PNEUMATEC.

RANGE SELECTOR FPRO CESS ERROR MQDEL INVENTORS LOUIS FRICKE JR. ROBERTA. vvALH FIG.3.

ATTORNEY Pmmdl 9 Sheets-Sheet 8 PROCESS F IG 3 F.

DEGBTAL VOLTMETEW INVENTORS LOUIS H. FRICKE, JR. ROBERT A. WALSHATTORNEY B SWAM 9 Sheets-Sheet 9 5.2 INPUT WAVE FlG. 6 a

MODEL OUTPUT FIG. 6 c

IE M

MG. 6 e

PROCESS OUTPUT JNVENTORS LOUIS H. FRICKE JR. ROBERT A. WALSH AT TOR NE YFUNCTIIGN GENETGE FUR PMI IDIUGIING SQUARE AND llAIt IF WAVE PULSES Thisapplication is a division of our copending application Ser. No. 495,565,filed Oct. 13, I965, and now US. Pat. No. 3,505,512.

This invention relates in general to certain new and useful improvementsin computer devices for determining process characteristics, and moreparticularly to a rapid process simulator which is capable of simulatingprocess conditions, and comparing the process conditions against a knownmodel of orthogonal functions.

In the design and development of controlled processes, there are twoareas of intense activity. The first of these areas lies in thetheoretical simulation of the total plant and the second of theseactivities lies in the empirical simulations involving the collection ofreliable experimental data to assist in the construction of a specialpurpose model. The simulation of a newly proposed process, even from thebest available theoretical basis is usually only an approximatesimulation. In most cases, it requires the employment of large andexpensive computer installations, either analog and/or digital computersso that by direct programming of design criteria, the optimum plantoperating conditions may be determined. These operating conditions maythen be used to construct a pilot plant scale model. However, even ifthe model were reliable, the scale-up problems produced are quitecomplex. In many cases, it is almost impossible to maintain exactrelationships between intrinsic parameters such as surface tension, heattransfer, etc. It is well established that few theoretical modelspresently existing can anticipate all of the significant processcharacteristics. As a result of these complexities, many full scaleplants are in need of partial redesigi.

All of the presently available modes of analyzing operating processesinvolve disturbing the process and determining the reaction from thedisturbance. The presently available methods generally employ asinusoidal type of process change when attempting to obtain processcharacterization. However, delays between the input signal and theoutput of the process may take a number of days. In fact, complete testsoften take months with the resultant upsetting of production. The newermethod of disturbing a process is through the use of a controlled pulse.The pulse is generally selected so that some of its harmonics canproduce a response of process output which yields all of the informationthat the sinusoidal techniques yield.

These pulse inputs and outputs can then be recorded and the data changedmathematically to Fourier transforms. The performance function, which isthe ratio of output to input in this transform, is the measure of thefrequency response of the entire system. This frequency response can, inturn, be depicted as a linear expression to show the relationship ofinput to output. This equation representing the performance functionrepresents the model in an analog-type of simulation. The procedure forfitting this linear model to a nonlinear system is sufficient to pennitthe devising of a correct control system within the normal range ofoperating conditions. However, Fourier analysis has the drawback ofbeing difficult to perform in commercially operating plants and thisfact makes a rapid description of the process difficult to obtain, ifnot unavailable. Moreover, if the process is complex and difficult to idescribe, the techniques presently employed are not able to describe allof the existing process characteristics. It is generally necessary toacquire the data from the process, to prepare the data in a form fortransformation by means of digital computer and then developing Fouriertransforms for the various signals to determine the harmonic values ofthe different frequencies. In general, it is often very difficult togive a precise physical interpretation of the various parametersaffecting the process from measurements in the field, when the processcharacteristics must be determined by use of both analog and digitalcomputer techniques.

It is, therefore, the primary object of the present invention to providea rapid process simulator for providing a determination of the dynamiccharacteristics of an actual process.

It is another object of the present invention to provide a rapid processsimulator of the type stated which is capable of determining both staticand dynamic characteristics of a process by comparing process conditionsto an established model and measuring the deviation therefrom.

It is a further object of the present invention to provide a rapidprocess simulator of the type stated which is capable of deriving simplelinear models for characterizing a controllable process.

lt is also an object of the present invention to provide a method ofdetermining an analytical description and characterization of anexisting process.

lt is another salient object of the present invention to provide a rapidprocess simulator of the type stated which is portable in nature andcapable of being transported to various locations for employment in amultitude of operating conditions.

With the above and other objects in view, our invention resides in thenovel features of form, construction, arrangement and combination ofparts presently described and pointed out in the claims.

in the accompanying drawings (nine sheets):

FIG. 1 is a front plan view of a rapid process simulator constructed inaccordance with and embodying the present invention and showing indetail the control panel thereof;

FIG. 2 is a schematic block diagram functionally showing the operativeconnection of the various component systems forming part of the rapidprocess simulator;

FIGS. 3a, 3b, 3c, Ed, 3e and 3f are a combined schematic wiring diagramshowing in detail the component systems forming part of the rapidprocess simulator, of which:

FIG. 3a schematically illustrates a triangular wave generator,

FlG. 3b schematically illustrates a pulse generator,

FIGS. 3c and 3d schematically illustrate a model of orthogonalfunctions,

FlG. 3c schematically illustrates an oscillatory transients generator,

FIG. 3e schematically illustrates an electrical and pneumatic rangeselector,

FIG. 3f schematically illustrates a summer, squarer, integrator, digitalvoltmeter and transducers;

FIG. d schematically illustrates the waveforms of the pulses produced bythe triangular wave generator and pulse circuits with respect to time;

FIG. 5 is a schematic wiring diagram showing an operative connection ofthe rapid process simulator to an unknown process; and 1 FIGS. tia, 6b,6c, 6d, and be illustrate the various waveforms produced in simulatingthe process of FIG. 5, wherein:

FIG. 6a represents the input waveform,

FlG. 6b represents the process output waveform,

FIG. he represents the model output waveform,

FIG. 6d represents the waveform on the output of the summer or the errorsignal,

FIG. he represents the waveform of the integral of the error squaredwith respect to time.

GENERAL DESCRIPTION The present invention relates to the use ofnoninteracting elements as a rapid method for determining processdynamics of a system. The rapid process simulator and the method ofemployment thereof is considered to be particularly adaptable for usewith linear stable processes whose dynamic characteristics are unknown.The unknown process is generally compared with an orthogonal model. Themodel is formulated with the idea of choosing a pulse input in such away to facilitate the construction of the system. The frequency analogsof the well-known Laguerre polynomials are particularly suitable as achoice for the simulator.

A five-telm orthogonal set has been found to be sufficiently adequate asa model for the simulator. A disturbing pulse is injected into an openloop system of the process and into the developed model of theorthogonal functions. The responses produced by the open loop system ofthe process and the orthogonal model is then compared by subtracting theresponse of the orthogonal model from the response of the unknownprocess which produces an error signal. The error signal is then squaredin a conventional squarer to produce the square of the signal and thenintegrated to obtain the integral of the error signal. The process canbe repeated with new values of the coefficient until minimization of theintegral error squared is obtained. This integral error squared can beconveniently depicted on a digital voltmeter. Moreover, the model andthe integrator can be provided with reset pulses from the triangular andpulse wave generators which are used to provide the disturbing pulses.When the best fit is obtained by observing the time histories of boththe unknown system and the model to the pulse input along with the valueof the integral, the coefficients are read out and a simple expressionis obtained for the input-output pair of interest.

In addition iff,(x) and f (x) are orthonormal, the following 0relationship is true In the past, sinusoidal waves have been used as ameans of providing disturbing pulses. The sinusoidal wave as a means ofproviding a disturbing pulse is no longer employed, inasmuch as atriangular wave generator providing a signal to a square wave samplerand a ramp wave sampler will provide all of the 2 5 harmonics necessaryfor the simulator. Accordingly, the rapid process simulator uses atriangular wave generator for developing pulses which are, in turn,transmitted to a pulse generator. The pulse generator employs a pair ofoff-on switching circuits, the first of which functionally serves as asquare wave generator or so-called sampler" or shaper and a ramp wavegenerator or so-called sampler or shaper. The second off-on circuitfunctionally serves as a delay square wave sampler and delay ramp wavesampler for handling transport delay times, that is where the inputpulse to the model is delayed so that the output of the unknown systemand the model will begin at coincident times. While the pulse generatoractually includes off-on switching circuits, these switching circuitscan be functionally realized in the manner as described, and moreovereach of the switching circuits is provided with pulse selectors forselecting a ramp wave or square wave as desired. Furthermore, each ofthe sets of square wave and ramp wave samplers is designed to providesignals to an electrical-pneumatic converter and range selector orpneumatic range selector. For example an electrical-topneumatictransducer can be employed for providing a pneumatic signal in theprocess or an electrical signal can be injected directly into theprocess and into the orthogonal model. Similarly, the output of theprocess can again be converted to an electrical signal for comparisonwith a model readout.

Once it has been established that the simple linear model issufficiently accurate to describe the process, it is routine todetermine the correct values of integral action, proportional action andderivative action on a standard process controller.

Such methods as the root locus method and methods of Bode and Black, andNyquist, etc. directly apply. Furthermore, the open loop adaptivecontrol function can be determined by establishing a simple linear modelfor different levels of operation. Thus, the necessary controllercharacteristics for the entire set of model functions can be found as afunction of these levels and with the application of thesecharacteristics the process will always be operating at an optimum.

The chemical systems are almost always nonoscillatory, that is, thetransfer function describing the dynamics are a series of time constantsin the denominator with real roots. After a mathematical expression forthe unknown process has been obtained through acquiring the coefficientof the parameter of the model, it is possible to formulate a procedureto obtain a slightly more damped closed loop response than theone-cypowers in the denominator and numerator. One then equates thecoefficients of like powers and solves for the controllercharacteristics.

ffifmmdb In these expressions f (x) and f (x are the conjugates of thereal functions f,(x) and f (x) respectively, and include real andimaginary components a f 1(R1jIX) and f RxjIx).

When an orthogonal set of functions is normalized, by setting ffimmm xand it will satisfy the second equation where the integral of thefunctions of x is equal to 1.

DETAILED DESCRIPTION Referring now in more detail and by referencecharacters to the drawings which illustrate a preferred embodiment ofthe present invention, A designates a rapid process simulatorsubstantially as illustrated in its compact portable form in the frontplan view of FIG. 1.

The rapid process simulator A can be designed as a rather small compactunit which is portable and easily transportable to various locations.Moreover, it can be designed so that it is capable of being fitted intoany of the standard electrical component racks. As illustrated in FIG.1, the rapid process simulator A is enclosed within a metallic cabinet 1which is snugly fitted within a portable housing 2 having ahandle-forming strap 3 on the upper end thereof. The housing 2 iscentrally provided with a large rectangular aperture 4 on the front facefor slidably accommodating the cabinet 1 of the rapid process simulatorA. The outer housing 2 may be conventionally provided with tracks androllers, as desired, for providing easy shifting movement of the cabinet1 into and out of the portable housing 2. This construction isconventional and is, therefore, not described in detail herein.

The cabinet 1 of the rapid process simulator A forms a control panel 5upon which are mounted a series of dials, switches and recorders, to behereinafter described in more detail. The control panel 5 is slightlyrecessed and extending around the periphery thereof on the cabinet 4 isa peripheral rim 6. A series of spaced conventional lock mechanisms (notshown) may be mounted on the front face of the housing and which engagethe rim 6 on the cabinet 1. These conventional lock mechanisms may beswingable from the locked position so that the cabinet 1 may be removedfrom the housing 2. Mounted on a side panel of the housing 2 is a pairof multistation terminal connectors 8 and a pair of pneumatic fittings9. Similarly extending from the rear wall of the housing 2 is a cord set10 for connection to a suitable source of electrical current (notshown).

Schematic Block Diagram FIG. 2 provides a schematic illustration inblock diagram of the operative connection between the various componentsystems forming part of the rapid process simulator and its operativeconnection to the process with unknown conditions. The rapid processsimulator A includes a regulated power supply S which supplies power forall circuits in all blocks of the instrument. A main off-on power switchs as illustrated in FIG. 1, is internally wired in this unit and mountedon the control panel 5. The simulator A also includes a triangular wavegenerator ill for producing pulses to be injected into an unknownprocess P having unknown parameters and into a model of orthogonalfunctions M. The triangular wave generator llll also includes a computetime mechanism 12 for adjusting the time period of the simulation. Thetriangular wave generator 111 provides the time controlling signal whichis transmitted to a pulse generator 13, as illustrated in FIGS. 2 and311. By reference to FIG. 3b, it can be seen that the pulse generator 13includes a pair of oft on bistable switching circuits I435 which aremore fully described in detail hereinafter. However, in the blockdiagram of FIG. 2, the pulse generator 13 is illustrated as including asquare wave generator or so-called sampler l6 and a ramp wave generatoror so-called samplcr" I7. The pulse generator I3 is also illustrated asincluding a delay ramp wave generator or sampler l8 and a delay squarewave generator or sampler I9. In terms of circuitry involved, thesamplers l6 and 17 are included in the switching circuit 115. Thetriangular wave generator 111 is illustrated as including four samplersfor ease of explanation of the invention since in functional form thegenerator 11 operates as though it included four samplers or wavegenerators. The triangular wave generator lll produces a triangular wavewhich is fed to the samplers 116, H7, 118 and 19, all in the manner asschematically illustrated in FIG. 2. The output of the triangular waveis always positive except for a short period when it is negative at theend of the compute cycle for resetting.

The square wave sampler l6 and the ramp wave sampler 117 are providedwith electrical output lines 20,21 respectively which can be connectedto an electrical range selector 22 for converting the signal into adesired electrical input range. The output lines 2&2] may also beconnected to an electrical-toprocess converter 23 which is capable ofchanging the electrical output into a desired process input. The processinput, of course, may be a pneumatic input or electromechanical inputand the converter 23 is designed to convert the electrical input thereofto the desired process input. As illustrated in FIG. 2, theelectrical-to-process converter 23 or so-called EP converter," is aconventional electropneumatic transducer capable of convertingelectrical signals into proportional pneumatic signals. Furthermore byreference to FIG. 3f, it can be seen that the electrical-to-processconverter 23 and the electrical range selector 22 are constructed withcommon circuitry and form a unitary electrical and pneumatic rangeselector. However, the electrical and pneumatic range selector isillustrated with the range selector 22 and converter 23 in block form inFIG. 2 since the selector serves both functions. This input signal whichmay be either in pneumatic or electrical form is thereupon inserted intothe process P in order to disturb the condition of the process. Thesignal is also inserted into the model M of orthogonal functions.However, it may be desirable to provide a delayed mode] signal incertain cases. Accordingly, the delay square wave sampler l8 and thedelay ramp wave sampler 19 are provided with outputs 24,25 which are, inturn, optionally connected to the input of the model M for providing asignal to the model M of orthogonal functions.

A two-way sampler switch 26 is connected across the output lines 20,21for selection of either a square wave signal or a ramp wave signal. Theswitch 26 is mounted on the control panel 5 in the manner as illustratedin FIG. 1. The switch 26 is, in turn, electrically connected to a switch27 which serves as an electrical-pneumatic selection switch, the latteralso being mounted on the control panel 5. By reference to FIG. 2, itcan be seen that the switch 26 functionally provides selection betweenthe square wave sampler l6 and the ramp wave sampler 17. The selectorswitch 27 provides selection between the electrical range selector 22and the process-range converter 23 for providing a desired pulse. Theoutput lines 24,25-are also provided with a sampler selection switch 28similar to the previously described switch 26 for selecting either adelay square wave or a delay ramp wave from the samplers 18,19

respectively. The switch 23 is mechanically connected to and operablewith the switch 26 and is, therefore, not mounted on the control panel.In other words, when the square wave sampler i6 is functionallyemployed, the delay square wave sampler 13 may be functionally employed,Similarly, when the ramp wave sampler I7 is functionally employed, thedelay ramp wave sampler 119 may be employed. A two-way switch 29 ismounted on the control panel 5 and is designed to functionally interposethe delay samplers I319 in the circuit by providing a delayed pulse tothe model M as illustrated in FIG. 2. It may be desirable to provide anoscillatory transient on the signal in the model function M if theprocess P contained such transients and therefore, an oscillatorytransients generator T is provided. The oscillatory transients generatorT is connected to the model of orthogonal functions M and into the inputline to the model M. A switch 39, which is mounted on the control panel5 provides optional interposition of the oscillatory transientsgenerator T in the system in the manner as schematically illustrated inFIG. 2.

The input signals are desigied to upset the process and, thereby,produce a process output signal which is, in turn, transmitted to aprocess to electrical signal converter 3ll or socalled "P-E converter."This converter is similar to the converter 23 and may be a conventionalpressure transducer. If the process P is electrical in nature and theoutput thereof is electrical, the output signal is transmitted directlyto an electrical range selector converter 32 substantially similar tothe previously described selector 22. The electrical range converter 32and the process-to-electrical signal converter 31 are functionallyillustrated in the bloclt diagram of FIG. 2 as separate components forpurposes of more fully describing the present invention. However, it canbe seen that these two components are partially combined to form anelectrical and pneumatic range selector as illustrated in FlG. 3e. Itshould also be noted that a selector switch is not employed for theoutput signals from the process since only an electrical or a pneumaticsignal may be transmitted therefrom.

The combined pneumatic and electric signal converter 31 transmits theoutput signal to one terminal of an adder or summer or so-calledtotalizer" 33 and the output signal of the model M is transmitted to theother terminal of the totalizer 33. An output tap 3d from theprocess-to-electrical converter 3i and an output tap 3d from the rangeselector converter 32 are connected to opposite terminals of anelectricalpneumatic selector switch 27'. Accordingly, it is possible toselect the proper signal from the process P for transmission to theadder 33. It should be recognized that the switches 27,27 are notconnected in common since it is possible to introduce an input signalwhich differs in kind from the output signal of the process. An outputtap 35 on the output side of the model M will provide the output signalof the model M. The adder 33 is designed to combine the output sig'ialof the model M of the orthogonal functions with the process signal and,thereby provide an error signal which can be tapped at 36 for opticalillustration thereof. The error signal from the adder 33 is transmittedto a conventional squarer 37 in order to obtain the square of the errorsignal with respect to time. The signal from the squarer 37 is thentransmitted to a conventional integrator 33 often referred to as anevaluation means" where the square of the error signal is integratedwith respect to time and, in turn, is transmitted to a four-placedigital voltmeter 39. The voltmeter 39 is provided with a four-digitreadout panel 39' mounted on the control panel 5, for direct readingoutput. The signal from the process P at the taps 34,34, the outputsignal from the model M at the tap 35 and the error signal at the tap 36can be graphically illustrated on a three channel oscillographicrecorder 30 or so-called recording oscillograph as illustrated inFIG. 1. This recorder is conventional in its construction and is,therefore, not described in further detail herein. The integrator 33which is conventional in its construction is also electrically connectedto the triangular wave generator ll3 for receiving reset pulses. Thedigital voltmeter 39, which is also conventional in its construction isnormally operating at its own repetition rate and, therefore, a numberof readings are monitored during one compute cycle. After the output ofthe error signal, which has been integrated, is depicted on the digitalvoltmeter 39, the triangular wave generator 11 is designed to providereset pulses to the integrator 38, the model M and the oscillatorytransients generator T for resetting each of these components to a zeroposition.

Thus, in the operation of the system, the unknown process which is to beanalyzed is selected. This process may be pneumatic, electrical,mechanical, biological, etc., the only criterion being that the processmust be capable of providing an electrical or pneumatic output signaland accepting an electrical or pneumatic input signal. The compute timemechanism 12 is set to a desired time period before pulses are injectedinto the process and into the model of orthogonal functions. This timecompute mechanism 12 controls the frequency of the triangular wavegenerator 11 which in turn provides a triangular wave signal to each ofthe square wave samplers 16,18 and to each of the ramp wave samplers17,19. If for the type of process being simulated, it is desirable toemploy a square wave, the switch 26 is shifted to the position where itcommunicates with the square wave sampler outlet line 20. If it isdesired to employ a delayed ramp or square wave for the model'M, theswitch 29 may be shifted to the position where the transport delaysamplers 18,19 are interposed in the circuit. Onthe other hand, if thesystem is such that a delayed wave to the model is not necessary, theswitch 29 is switched to the off position so that the transport delaysamplers 18,19 are inoperable, that is the off-on switching circuit isrendered ineffective through the switch 29. After the selection betweenthe square wave and ramp wave samplers, the switch 27 is shifted to theconverter 23 or the range selector 22. The converter 23 is employed ifthe signal is one other than an electrical signal. However, if the inputsignal is an electrical signal, the range selector 22 would be employed.If an input signal is transmitted to the process and by inspection ofthe recorder, the process output is found to contain oscillatorytransients, the oscillatory transients generator T may be interposed inthe system by closing the switch 30, that is shifting the switch 30 toeither plus" or minus" position.

The responses produced by the open loop system of this process P and theorthogonal model M is compared by subtracting the response of theorthogonal model M from the response of the process P at the summer 33,which in turn produces an error signal at 36. The signal from theprocess can be tapped at 34,34 and the signal from the model can betapped at 35. If the signal from the process P is other than anelectrical signal, it is converted to an electrical signal in the P-Econverter 31. The error signal on the output of the adder 33 is thentransmitted to the squarer 37 where it is squared. The integral of theerror squared is then obtained in the integrator 38 and this errorsquared signal is transferred to the digital voltmeter 39 where anoutput reading is obtained. By observing the time histories of both theunknown process P and the model M, the coefficients of the parameters ofthe model with respect to time are obtained and at the smallest errorsignal, a simple expression is obtained for the input-output pair ofinterest.

Having described the overall operation of the various component systems,it is possible to describe each of the component systems in detail.

Triangular Wave Generator The first component system in the triangularwave generator which is schematically illustrated in FIG. 3a. Thetriangular wave generator 11 is connected to the power supply S andreceives therefrom a plus reference sigtal and a minus reference signalby means of reference signal conductors 41,42 respectively. Theconductors 41,42 are connected across contacts 43,43 of a relay 44.Movable between the contacts 43,43 is a contact arm 45 which isconnected dard potentiometer 46 forms part of the compute time controlmechanism 12 and'a control dial 46' is mechanically connected theretoand mounted on the control panel 5 for operation of the same. Themovable arm of the potentiometer 46 which forms part of the compute timecontrol mechanism 12 is connected through an integrator input resistor47 to a resetoperate switch or so-called mode control switch 48 formingpart of a Miller Integrator 49. The Miller Integrator 49 includes anoperational amplifier 50 and connected in parallel therewith is a seriesof integrating capacitors 51. A series of time scale switches 52 arealso connected in parallel therewith and are designed to control theintegration rate of the integrator 49. A reset resistor 53 is alsoconnected in parallel to the amplifier 50 and is connected to oneterminal of the resetoperate switch 48 for the purpose of resetting theintegrator 49 to zero. The reset-operate switch 48 is actually a modecontrol and is mounted on the control panel 5 in the manner as shown inFIG. 1. In order to make time scale changes and get proper input andoutput characteristics, the reset-operate switch 48 is set to the resetposition, that is the lower position, reference being made to FIG. 3a.When shifted to the operate position, that is the upper position,reference being made to FIG. 3a, the integrator and associated circuitryhereinafter described will continually provide triangular wave signals.

Also connected across the plus and minus reference conductors 41,42 area pair of voltage dividing variable resistors 54,55, the movable arms ofwhich are connected to contacts 56,56, respectively. A contact arm 57movable between the contacts 56,56 is connected through an inputresistor 58 to a summing junction 59 of an operational amplifier 60. Aninput resistor 61 is located on the opposite side of the summingjunction 59 with respect to the amplifier 60. In effect, a comparison ofvoltage across the input resistors 58,61 is made with the summingjunction 59. The voltage sum is amplified by the amplifier and if thesign is correct, the signal is passed through a diode 62 to a relay coil63 forming part of the relay 44. If the sign is not correct, the voltagewill not pass through the diode 62 but is shunted to the summingjunction 59 through a diode 64 connected in parallel with the amplifier60.

A three-position pulse direction switch 65 having a plus position, aminus position and an off position is connected across the referenceconductors 41,42. The switch 65 is mounted on the control panel 5 andthe movable element thereof is connected to a contact 66 which iscooperative with a movable contact arm 67, the latter being connected toa height/rate potentiometer 68. A height/rate control dial 69 ismechanically connected to the potentiometer 68 for operating the sameand is mounted on the control panel 5.

When the main power switch s is closed, the reference conductors 41,42will become energized. The contacts 43,43 and 56,56 will also becomeenergized. If the pulse direction switch 65 is moved to the positiveposition, the contact 66 is energized. The deenergized position of therelay 44 is illustrated in FIG. 3a. If the reset-operate switch 48 is inthe operate position, the integrator 49 will produce a positivelyincreasing output signal. This voltage is compared by the inputresistors 58,61 to the voltage on the variable resistor 54. When theoutput voltage on the integrator 49 reaches a value slightly morepositive than the negative value on the variable resistor 54, then thesign of the amplifier 60 is negative allowing current to pass throughthe diode 62 and thus energizing the coil 63 of the relay 44.Energization of the coil 63 will cause the contact arms 45,57 to shiftto the contacts 43,56' respective- 1y. This changes the value of theinput to the integrator 49 changing the sense thereof so that it becomesincreasingly negative. The output voltage of the integrator 49 becomesincreasingly negative until the voltage compared at the summing junction59 is slightly negative causing the output of the amplifier to bepositive. Since the diode 62 will not accept positive voltages, thiscauses the coil 63 to become deenergized. As a result thereof, thecontact arms 45,57 and 67 will shift to their directly to the computetime control mechanism 12. A stanupper position, reference being made toFIG. 3a. The diode 64 is connected so that the amplifier 60 receivesnegative feedback when the output thereof attempts to become positive.The presence of the contacts 66 insures that a pulse will only begenerated when the output of the integrator 49 is increasing positively.By reference to FIG. 3a, it can be seen that the relay coil 63, thediodes 62,64, the amplifier 69 and the input resistors 58,61 formv arelay comparator circuit which is present in many other componentsystems of the present invention. This relay comparator circuit issimilar to the relay comparator circuit used in the other systems andis, therefore, not described in detail hereinafter, However, it shouldbe recognized that more input resistors can be employed for comparingmore than two circuits.

7 Mode Control Circuit Many reset relay circuits are present in thecomponent systems forming part of the rapid process simulator such asthe model M, the oscillatory transients generator T and the integrator39. A mode control circuit, substantially as illustrated in FIG. 3a, isprovided for resetting each of these component systems to initialconditions after each compute cycle. The mode control circuit includes apair of low voltage relay power conductors 69,70. This relay power issupplied to the various relay coils by means of closing the manualreset-operate switch 48 or automatically at the end of the compute cycleby means of contacts 71,71 forming part of a relay 72. The relay 72 isenergized by a relay comparator circuit 73 similar to the relaycomparator circuit in the triangular wave generator 11. When thetriangular wave becomes slightly negative, the relay 72 will becomeenergized causing the contacts 71' to close and this, in turn, willenergize all other reset relay coils in all component systems, therebyresetting the associated component systems. The operative connection tothe other component systems of the mode control circuit will be morefully hereinafter described in detail.

A typical relay comparator circuit as employed in the present inventionis illustrated in FIG. 3a and includes a relay coil such as the coil 72which operates a set of contacts similar to the contacts 71,71. Thetypical relay comparator circuit, therefore, includes the relay coil 72,an operational amplifier 74, a pair of diodes 75,76, and at least twoinput resistors 77,77. The diode 75 is connected in parallel with theoperational amplifier 74 and the diode 76 is connected in series withthe amplifier 74 and the relay coil 72. In its operation, the amplifier74 will amplify a difference signal measured by the input resistors77,77. If the difference signal is of the proper polarity, the diode 76will conduct, thereby energizing the coil 72. If the difference signalis of an undesired polarity, the diode 76 will not conduct and the diode75 will conduct thereby maintaining a low output from the amplifier 74preventing energization of the relay 72. Connected to the resistor 77 isan internally disposed reference potentiometer 77 for providing aslightly positive voltage so that the relay 72 will be energized whenthe triangular wave is slightly negative. By means of this circuit, itis possible to compare a selected fixed or variable voltage to areference voltage and performing either of two functions depending uponthe difference in the magnitude of these two voltages.

Pulse Generator The functional operation of the pulse generator 13 ismore fully illustrated in FIG. 2 and the operation thereof in terms offunction is described hereinabove. The components forming part of thepulse generator are more fully illustrated in FIG. 3b and include fourrelay comparator circuits 78, 79, 80 and 81. Each of these relaycomparator circuits 78, 79, 99 and 81 is substantially similar to therelay comparator circuit 73. These relay comparator circuits are alsosubstantially similar to the comparator circuit in the triangular wavegenerator 11 except that the relays are energized on a positive signalwhereas the relay in the comparator circuit of the triangular wavegenerator was energized on a negative signal.

The input of each of the relay comparator circuits 79, 79, 89 and 81 isconnected in common to the output of the integrator 49. Moreover,another input of each of the relay comparator circuits 78, 79, 99 and 91is connected to the movable element of a delay control potentiometer 82.One terminal of the delay control potentiometer 82 is connected to aminus reference conductor 93 which in turn receives power from the powersupply S. The opposite terminal of the potentiometer 82 is grounded. Thedelay control potentiometer 82 is operable by a delay control dial 94mounted on the control panel 5 and is designed to provide a delay in thetime that the first disturbing pulse commences after the operate switchis shifted to the operate" position.

The relay comparator circuits 79,91 have additional input resistors97,99 which are connected in common and to the movable arm of a durationcontrol potentiometer 96. One terminal of the duration controlpotentiometer 96 is connected to the negative reference conductor 83 andthe opposite terminal thereof is grounded. The movable arm 85 of theduration control potentiometer 96 is mechanically connected to andoperably by a duration control dial 96', the latter being mounted on thecontrol panel 5. The duration control potentiometer 96 is designed toprovide any desired pulse widths for both square and ramp wave pulsesand associated delayed square and ramp wave pulses. The relay comparatorcircuits 99,91 and additional input resistors 89,90 respectively, areconnected in common to the movable arm 91 of a transport delay controlpotentiometer 92. The movable arm 91 of the potentiometer 92 ismechanically connected to and operable by a transport delay control dial93, which is mounted on the control panel 5. The transport delay controlpotentiometer 92 is designed to control the time delay between theinitiation of a disturbing pulse to the model M after the injection of adisturbing pulse into the process P. The relationship between thedisturbing pulse transmitted to the process P and the pulse transmittedto the model M for comparison is more fully illustrated in FIG. 2.

The relay comparator 78 includes a set of normally open contacts 94,94and the relay comparator 79 includes a pair of normally closed contacts95 and a normally open contact 95. Similarly, the relay comparatorcircuit includes a pair of normally closed contacts 96 and a normallyopen contact 96' and the relay comparator circuit 91 includes a pair ofnormally closed contacts 97 and a normally open contact 97. The normallyopen contact 94' is connected through an input resistor 99, through thenormally closed contact 95, and to the input of a medium gainoperational amplifier 99. The movable arm of the selector switch 26 isconnected to the output side of the amplifier 99 and to the normallyopen contact Connected to the input side of the amplifier 99 is afeedback resistor and also connected in parallel with the amplifier 99is a feedback capacitor 191. Thus, when the sampler switch 26 is shiftedto the upper position, the feedback resistor 190 is inserted in thecircuit and the amplifier 99 operates as an inverter. When the switch 26is shifted to the lower position, the capacitor 101 is inserted in thecircuit and the amplifier 99 operates as an integrator. The operationalamplifier 99, the feedback resistor 109 and the capacitor 101, incombination with the selector switch 26 constitutes a pulse selector.

A similar pulse selector is connected to the relay comparator circuits80,91. The contact 96 is connected through an input resistor 102,through the normally closed contact 97 to the input of a medium gainoperational amplifier 103. The selector switch 28 is connected to theoutput of the amplifier 1193 and to the normally open contact 97.Connected to the input of the amplifier 193 is a feedback resistor 104and a feedback capacitor 105. As previously indicated, the switches26,28 are ganged or connected in common, so that they operate in unison.Thus when the switch 26 is shifted to the upper position, the switch 28will be shifted to the upper position and the amplifiers 99,103 willboth function as inverters. Similarly, when the switch 26 is shifted tothe lower position, the switch 28 will be shifted to the lower position,reference being made to FIG. 3b and the amplifiers 99,103 will serve asintegrators. By further reference to FIG. 3b, it can be seen that theoutput of the operational amplifiers 99,103 is connected to thetransport delay switch 29.

It can be seen that the relay comparator circuits 78,79 combined withthe associated pulse selector circuit forms the square wave and rampwave selectors 16,17. Similarly, the relay comparator circuits 80,81 andthe associated pulse selector circuit form the delay square wave anddelay ramp wave selectors. In its operation, the triangular wave willincrease positively in slope to a point where it equals the value set onthe delay control potentiometer 82 at which time the contact 94 closes,thereby feeding a voltage from the height/rate potentiometer 68 to theinput resistor 98. Since the contacts 95 are closed at this time, thissignal will be transmitted to the amplifier 99. In similar manner, whenthe positively increasing triangular wave voltage equals the combinedvoltages maintained on the delay control potentiometer and the durationpotentiometer 85 the contact 95' will close. This will remove the inputto the amplifier 99 and resets the amplifier 99 to a zero position.During the time that the triangular wave is increasing positively, aconstant amplitude signal is transmitted to the relay comparatorcircuits 78,80 from the height/rate control potentiometer 68. Thus, bythe continued switching of the on-off switching circuit 14, the adjustedconstant amplitude signal to the relay comparator circuit 78 willproduce a square wave when the selector switch 26 is shifted to thesquare wave position, that is the upper position. In this manner, theamplifier 99 serves as a coupler. When the switch 26 is shifted to thelower position, that is the ramp wave position, the amplifier 99 willserve as an integratorcoupler and the constant amplitude signal suppliedto the relay comparator circuit 78 will form a ramp wave whenintegrated.

The off-on switching circuit operates in similar manner to the off-onswitching circuit 14. More specifically, the relay comparator circuits80,81 operate in a manner similar to the operation of the relay circuits78,79. When the voltage at the contact 96 is equal to the combinedvoltage at the delay control potentiometer 82 and the transport delaycontrol potentiometer 92, the contact 96 will close. The same signal fedto the contact 94 is fed to the contact 96 and the input resistor 102.This signal is transmitted to the amplifier 103. Therefore when theselector switch 28 is shifted to the upper position, the amplifier 103serves as an inverter and a square wave signal is produced. When theselector switch 28 is shifted to the lower position, the amplifier 103serves as an integrator and a ramp wave signal is produced. However, thesignal output of the amplifier 103 is delayed more than with respect tothe amplifier 99. This occurs as a result of the interposition of theresistors 89,90 in ,the circuit, thereby causing the relay comparatorcircuits 80,81 to operate on a higher voltage of the triangular wavesignal.

From the above analysis, it can be seen that by increasing the voltageon the delay control potentiometer 82, a higher voltage is required atthe other input of the comparator circuit 78 to cause the contact 94' toclose. This will create a greater delay in the time that the square wavecommences. In similar manner, an increase of voltage in the durationcontrol potentiometer 86 will require a greater voltage on thetriangular wave input to the relay comparator circuit 79 before the samewill switch. Also, an increase in voltage on the transport delaypotentiometer 92 will necessitate a larger voltage on the triangularwave input to the relay comparator circuits 80,81 before the same willswitch. In this manner, it is possible to control the delay and durationof the initial square wave or ramp wave signal and to control the delay,duration and transport time of the second square or ramp wave signal. Byshifting the switch 29 to the lower position, that is the on position,the transport delay square and ramp wave selectors 18,19 are inserted inthe circuit. By shifting the switch 29 to the upper position, that isthe 011 position, no transport delay is created and square or rampwavesignals will be fed simultaneously to the model M, the oscillatorytransients generator T and the process P.

Model The model is designed to match an unknown process in order todetermine the parameters of the dynamic characteristics of the process.In the rapid process simulator A, the

Output a a 1 T 8) Input (8) It can be seen that the mathematicalexpression of the model includes parameters in a fifth order system ofwhich five are amplitude coefficients and five are time constants. Themathematical theory for the derivation of the circuit requirements to bethe analog of this expression is set forth hereinafter. However, itshould be recognized that a higher order system could be employed insome cases where it is necessary to obtain a more accurate simulation ofthe system. It should also be recognized that the model herein describedis orthogonal to a unit input function. For any other practical inputpulses, the degree of orthogonality is reduced slightly. This reductionin orthogonality by employment of other than unit input pulses hasproduced no problem and the model set forth above has been found to beadequate. If it is desired to use ,a greater degree of mathematicalrigor, it is possible to adjust the model within the scope of thisinvention by altering the present model and testing the alterationthereof mathematically for orthogonality. The method of altering themodel will be more fully understood by reference to the mathematicaltheory of operation of the rapid process simulator hereinafter setforth.

The present model includes five amplitude constants a,, 11,, a a a andfive time constants T,, T T T T The circuitry in FIGS. 30 and 3d, whichis a representation of this mathematical model, is designed to providedirect readouts for each of the 10 parameters.

The circuit of the model, therefore, includes five modules 106, 107,108, 109, 110, each of which produces a readout of one amplitudecoefficient and one time constant for each order. Each of the modules106-110 is substantially similar in construction and operation and,therefore, only the module 106 will be described in detail. The module106 includes a summer 111 formed by an operational amplifier 112, aninput resistor 113 and a feedback resistor 114. The amplifier 112 alsoincludes an input resistor 115. It can be seen that the input resistor113 is connected directly to the output from the pulse generator 13. Theoutput of the operational amplifier 112 is connected to one terminal ofa time constant potentiometer 116, the other terminal of thepotentiometer 116 being grounded. The potentiometer 116 is provided witha control dial 116' mounted on the control panel 5. The movable elementof the potentiometer 116 is connected to the input resistance 117 of anintegrator 118. The integrator 118 includes an operational amplifier 119and a feedback capacitor 120. Interposed between the movable element ofthe potentiometer 116 and the input of the operational amplifier 119 area pair of reset contacts 121, which are operable by a relay reset coil122. The reset relay coil 122 is operatively connected to and operableby the mode control circuit described hereinabove. Also connected infeedback relationship with the contact 121 is a feedback resistor 123,which is designed to reset the integrator to a zero position after eachcompute cycle. The module 106 also includes an inverter 124, which isconnected to the output side of the operational amplifier 119. Theinverter124 includes an operational amplifier 125 having an inputresistor 126 and a feedback resistor 127. The output of the inverter 124is connected through the resistor 115 to the input of the summer 111.

The input from the pulse generator 13 feeding the summer 111 through theinput resistor 113, in conjunction with the integrator 118 and theinverter 124, will simulate the transfer function of a system describedby a first order differential equation. Connected in parallel with theinverter is a direction switch 128 having a plus" position, a minus andan off position. The direction switch 128 is designed to provide propersense of the module simulation with regard to the unknown process. Thedirection switch 128 is mounted on the control panel 5 for operationthereof. At the output of the switch 128, the circuit thus far describedwill have transfer characteristics of a first order system with anamplitude coefficient of plus or minus one. In order to provide numbersother than one as an amplitude coefficient, the movable element of theswitch 128 is connected to an amplitude potentiometer 129 having acontrol dial 129' mounted on the control panel 5. The movable element ofthe potentiometer 129 is connected through an input resistor 130 to asummer or total izer 131. The totalizer 131 may have a gain greater thanone and of any desired value on the various inputs as constructed. Thepotentiometer 129 is connected so that it can select any portion of thegain of the totalizer 131. The gain between the input of the module 106and the output of the switch 128 is one. The potentiometer 129 providesa selection of any number less than one to be multiplied by the fixedgain in the associated input of the totalizer 131. The value of a is,therefore, equivalent to the position of the potentiometer 129multiplied by the fixed gain of the totalizer 131.

By reference to FIGS. 30 and 3d, it can be seen that each of the modules106-110 is substantially similar in construction. The method ofcalculating the amplitude coefficient in each module 107-110 issubstantially similar to the method employed in determining theamplitude coefficient in the module 106. Thus, the module 107 isprovided with a direction switch 132 having an off position, a plusposition and a minus position. The direction switch 132 is designed toprovide the proper sense of the amplitude coefficient a in the module107 with regard to the unknovm process. Each of the modules 108, 109,110 is also provided with direction switches 133, 134 and 135respectively. Each of the direction switches 133, 134 and 135 isdesigned to provide the proper senses of the amplitude coefficients a a11 in each of the modules 108, 109, 110 with regard to the unknownprocess. Moreover, by reference to FIG. 1, it can be seen that each ofthe direction switches 132-135 is mounted on the control panel 5. Themovable elements of each of the direction switches 132, 133, 134 and 135are connected to amplitude potentiometers 136, 137, 138 and 139respectively, having control dials and all of which are mounted on thecontrol panel 5. Each of the potentiometers 136-139 is similar to thepotentiometer 129 and are connected through input resistors 140, 141,142 and 143 respectively to the totalizer 131.

The totalizer 131 comprises a medium gain operational amplifier 144 anda feedback resistor 145 connected in parallel therewith. The totalizer131 also includes the five input resistors 130, 140, 141, 142 and 143.The values of the various input resistors 130 and 140-143 are sized togive a proper gain constant with respect to the feedback resistor 145 sothat the various ranges of the amplitude coefficients a -a can beassigned to the respective potentiometers 129 and 136-139. It can thusbe seen that the values of each of a a a a is equivalent to the positionof the respective potentiometers 136, 137, 138 and 139 multiplied by thefixed gain of the totalizer 131.

As indicated above, each of the modules 106-110 includes a summer, anintegrator and an inverter. The summer of the module 107 includes anamplifier 146 having an input resistor 147 which is connected to theoutput of the integrator 118 in the module 106. The amplifier 146 isalso provided with an input resistor 148 which is connected to theoutput of the summer 111 in the module 106. In similar manner, themodule 108 is provided with an amplifier 149, which is connected throughinput resistors 150,151 to the outputs of the integrator and summerrespectively of the module 107. The summer of the module 109 is providedwith an operational amplifier 152, which is connected through inputresistors 153,154 to the outputs of the integrator and summerrespectively of the module 108. Finally, the summer of the module isprovided with an amplifier 155, which is connected through inputresistors 156,157 to the outputs of the integrator and summer,respectively, of the module 109. Each of the modules 106- -110 wouldprovide the same form of input over output characteristic if theconnecting input resistors 148, 151, 154 and 157 were removed. Thetransfer function of the integrator is Us. From a study of the feedbackrelations in each of the modules 106-110, it can be seen that theresistor 148 supplies the term [T, s] and the resistor 147 provides theterm l/T,s1 when combined with the associated summer in the modelequation. In similar manner, the resistor 151 provides the term [T andthe resistor provides the term l/T r +1 when combined with theassociated summer; the resistor 154 supplies the term [T the resistor153 supplies the term 1 /T s+l when combined with the associated summer;the resistor 157 supplies the term [T and the resistor 156 supplies theterm 1/T s-l-l when combined with the associated summer, in the modelequation. The module 110 supplies the value l/T s+l. It can be seen thatby going through each module the output of said module is equivalent tothe input of the module multiplied by the characteristic function ofsaid module. Thus, the output of the fifth module 110 is the product ofall modules 106-110 characteristic function times the input signal.

By further analysis of the circuit in FIG. 30 and 3d, it can be seenthat the output of the first module 106 produces the normalized firstterm in the orthogonal set, namely llT sl-l; the output of the module107 produces the normalized second term in the orthogonal set, namelythe output of the module 108 produces the normalized third term in theorthogonal set, namely the output of the fourth module 109 produces thenormalized fourth term in the orthogonal set, namely and the output ofthe fifth module 110 produces the normalized fifth term in theorthogonal set, namely The terms in this orthogonal set are orthonormalbecause each amplitude coefficient a is one in the above case. In otherwords when all modules are connected together in the manner as shown inFIGS. 3c and 3d with the exclusion of the amplitude potentiometer, anorthonormal set is produced. When the totalizer 131 is included and the0 functions are not equal to one, an orthogonal set is produced.

The summer amplifiers 146, 149, 152 and in each of the modules 107, 108,109, 110 has outputs connected directly to time constant potentiometers158, 159, 160, 161 respectively. The opposite terminals of each of thesepotentiometers 158- 161 are grounded. Furthermore, the movable arms ofeach of the potentiometers 158-161 are connected to reset con tacts 162,163, 164 and 165. The time constant potentiometers 158, 159, 160 and 161as well as the time constant potentiometer 116 are mounted on thecontrol panel in the manner as illustrated in FIG. 1.

In order to understand the operation of each of the modules 106 1 indetermining the time constant T, it is necessary to consider each ofthese modules separated at the connecting resistors such as the inputresistors 147,148. Thus, the module 106 would be considered without theresistors 147,148 and the module 107 would be considered as includingthe input resistors 147,148 and excluding the input resistors 150,151.Each of the modules 106110 when considered in the autonomous stateoperates in like manner and, therefore, the operation of one module isdescribed in detail herein.

Considering the module 106, the module includes the summer 111, the timeconstant potentiometer 116, the integrator 118 and the inverter 124. Inorder to understand the theory of the production of the time constant,it is necessary to briefly set forth the mathematical theory of eachmodule. The summer 111 takes each of two input signals, combines thesignals, inverts the combined signal and presents the results on itsoutput. The potentiometer 116 receives the output signal from the summer111 and produces a proportional amount of the summer 111 output as itssignal which is dependent upon the potentiometer setting. The outputsignal from the potentiometer 1 16 is integrated with respect to timeand inverted by the integrator 118 and is presented on the output of theintegrator 118. The signal from the output of the integrator 118 isinverted through the inverter 124 and is presented as one of the inputsto the summer 111. From the analysis of the following relationships, itcan be seen that the time constant T is produced. It is desirable tofind the integrator output voltage from the module 106 in terms of theinput voltage. It is also desirable to find the sum of the outputvoltage and the feedback voltage to the summer in terms of the inputvoltage. If K represents the potentiometer setting and T represents thetime constant, then Moreover, if e is equal to the integrator outputvoltage and e,

is equal to the input voltage, it can be proved that:

In order to determine the sum of the summer output voltage and theintegrator output voltage in terms of the input voltage, it is onlynecessary to find the summer output voltage in terms of the inputvoltage and add the same to the output voltage in terms of the inputvoltage. Permitting e, to represent the summer output voltage, it can beproved by the analysis of the above circuit that:

1 Adding each of the above output voltage relationships, it can be seenthat the sum of the summer output voltage and integrator output voltagein terms of the input voltage is equal to:

in in l e, =summer output voltage of module 106 e, =summer outputvoltage of module 107 e. =su'mmer output voltage of module 108 e,=summer output voltage of module 109 e, =summer output voltage of module110 T =time constant of module 107 T =time constant of module 108 T=time constant of module 109 T =time constant of module 110 Thus, it canbe seen In similar manner, the additional model sets can be written forthe remaining terms in the model equation. It can thus be seen 0 thatproduced by the module 109 and by the module 110 are produced in likemanner. Accordingly, from the above analysis, it can be seen that eachof the amplitude coefficients and each of the time constants areproduced by the five modules 106-110 in combination in the model M.

produced Oscillatory Transients Generator The orthogonal model M ashereinabove described is only capable, of simulating a system with realroots in the denominator of its characteristic equation. In someprocesses, imaginary roots exist in the denominator of this samecharacteristic equation and this is exhibited by oscillatory transients.In order to accurately simulate processes of this latter type, it isnecessary to provide a simulation of the oscillatory transient on thesignal from the model. The oscillatory transients generator T isconnected in parallel with the model M and may be optionally interposedin the circuit by means of the switch 30. By reference to FIGS. 2 and30, it can be seen that the switch 30 is a three position switch, havinga plus, minus and off position. The transients generator is designed toproduce a sinusoidal output of selected frequency and damping. Thetransients generator T is also designed to provide a variable phaseshift of up to 90. The switch 30 will provide a phase shift of 180 andcoupled with the 90 phase shift can provide a complete effective phaseshift of 360. It is known that the solution of the following secondorder differential equation is an oscillatory variance in the variablex.

da: cit where m is the undampened natural frequency and C is the dampingratio. If p is substituted for d/dt, the characteristic equation may bewritten as:

p l-2w p+w from which the two roots are When l, the system has complexroots and the oscillatory response is given by the equation where =tan90 Therefore, the equation can be written as The oscillatory transientsgenerator circuit as illustrated in FIG. 30 is an analogue of thesolution to the above second order differential equation.

The oscillatory transients generator T comprises an inverter 166, theinput of which is connected directly to the output of the pulsegenerator 13. The output of the inverter 166 is connected directly tothe switch 30 which is, in turn, connected to the input of a summinginverter 167. The inverter 166 in combination with the switch 30 isdesigned to provide the 180 phase shift of the output signal from thetransients generator T. The output of the summing inverter 167 isconnected to a frequency adjusting potentiometer 168 having a controldial mounted on the control panel 5. The movable arm of thepotentiometer is connected to a summing integrator 169 which integratesthe signal from the potentiometer 168. The output of the summingintegrator 169 feeds a second potentiometer 170 which is mechanicallyconnected to and operable with the potentiometer 168 in the manner asillustrated in FIG. 3c. The potentiometer 170 also adjusts thefrequency. In effect, therefore, the two potentiometers 168 and 170operating in tandem provide frequency adjustment. The output of thepotentiometer 170 is, in turn, connected to a second integrator 171 andthe output of the integrator 171 for feedback to one of the inputs ofthe summing inverter 167. A decay control potentiometer 172 having adial mounted on the control panel 5 is connected to the output of thesumming integrator 169 and to an input thereof. The decay controlpotentiometer 172 provides values of the damping ratio 1; from 0 to 1.If the decay control potentiometer 172 is set at a 0 position,continuous oscillation would exist and if it were set at a maximumposition of 1, critical damping would occur. A phase controlpotentiometer 173 has a pair of terminals, one of which is connected tothe integrator 169 and the other of which is connected to the integrator171. The potentiometer 173 has a control dial mounted on the controlpanel 5. The phase control potentiometer 173 is designed to combine theoscillatory output of the integrator 169 and the output of theintegrator 171 which has been delayed The movable arm of the phasecontrol potentiometer 173 is connected to the input of an inverter 1741.By shifting the movable arm of the potentiometer 173 through its entirespan, it is possible to obtain a change in phase of 90. The output ofthe inverter 174 is connected to an amplitude control potentiometer 175having a control dial mounted on the control panel 5, the opposite endof the potentiometer 175 being grounded. The movable arm of thepotentiometer 175 is connected. through an input resistor 175' to theinput of the amplifier 1 141 in the summer 131. The amplitude controlpotentiometer 175 is designed to vary the total amplitude of theoscillatory signal from the oscillatory transients generator T. Theintegrator 169 and the integrator 171 are provided with reset relaycontacts 176, which are operable by a reset relay coil 176 for resettingof the oscillatory transients generator T after each compute signal. Therelay coil 176 is connected to and operable by the mode control circuitin the manner as previously described.

Electrical and Pneumatic Range Selector By reference to FIGS. 2, 3d and32, it can be seen that the signal from the pulse generator 13 istransmitted through a summer 177 to the selector switch 27 wheretransmission may be optionally directed to either the electrical rangeselector 22 or the electrical-to-pneumatic transducer 23. The blockdiagram of FIG. 2 provides aschematic illustration of the function ofthe combined electrical and pneumatic range selector, the circuitry ofwhich is illustrated in FIG. 3e. The circuit, however, is combined sothat the range selector 22 and the converter 23 function as a unitarycomponent system. In like manner, the output of the process P isdirected to the range converter 32 and pneumatic-to-electric transducer31 in the block diagram of FIG. 2. Again, this is a functionalillustration and these two components are combined in the electric andpneumatic range selector of P16. 32. in essence, the two converters23,31 and the two range selectors 22,32 are combined to form theelectrical and pneumatic range selector. However, by reference to FIG.3e, it can be seen that the upper portion of the circuit provides aselection of the desired signal to the process and the lower portion ofthe circuit provides a selection of the desired signal from the process.

The summer 177 comprises an operational amplifier 178 with an inputresistor 179 and a feedback resistor 180 so that the summer 177 alsoserves as an inverter. Also connected to the input of the amplifier 178is an input resistor 181, which is also connected to the movable elementof a static process position potentiometer 182 having a control dial 183mounted on the control panel 5. One terminal of the potentiometer 182 isconnected to a minus reference voltage from the power supply S and theopposite terminal of the potentiometer 182 is grounded in the manner asshown in FIG. 3e. Connected to the output of the amplifier 178 is aconventional voltmeter 184 having a dial face 185 mounted on the controlpanel 5 and which is designed to show the operating level of the processP. The output of the amplifier 178 and the voltmeter 184 is, in turn,connected to the movable element of the switch 27. The static processposition potentiometer 182 and the voltmeter 1841 are designed toprovide the same reference level input signal from the pulse generator13 on which the process P normally operates.

The switch 27 is a two position switch having an electrical position anda pneumatic position. By reference to FIGS. 1 and 3e, when the switch 27is shifted to the pneumatic" position (lower position), the signal fromthe output of the summer 177 is transmitted to the electrical-pneumaticor E-P transducer 23. lnterposed between the switch 27 and thetransducer 23 is a pneumatic range selector switch 186 having aplurality of pneumatic input ranges. The switch 186 is designed to havethe ranges which are commonly found in pneumatic control systems. In thepresent application, a twoposition pneumatic range selector switch hasbeen adopted since the vast majority of pneumatic control systemsoperate on a 3-15 p.s.i.g. or a 6-30 p.s.i.g. range. The output of thetransducer 23 is provided with the pneumatic fitting 9 for optionalconnection to the process P. In this connection, it should be understoodthat the transducer 23 may be provided with more than one setting forvariable situations.

When the switch 27 is shifted to the electrical position (upperposition), the switch 27 is connected to a voltage divider circuitconsisting of fixed resistors 187,188. Connected to the common terminalof the resistors 187,188 is a multiple position, rotary, electric rangeselector switch 189 having a desired electrical range at each rangeposition. The pneumatic range selector switch 186 and the electricalrange selector switch 189 have control dials 190,191, respectively whichare mounted on the control panel Sin the manner as illustrated inFIG. 1. By further reference thereto, it can be seen that the rangeselector switch 189 herein employed is provided with four positions,namely a l milliamp position, a 1050 milliamp position, a l5 voltposition and a 1--9 volt position.

The movable element of the range selector switch 189 is connected to acurrent voltage converter 192 which includes a summer inverter 193formed by an operational amplifier 194 with an input resistor 195 and afeedback resistor 196. The voltage current converter 192 also includes asecond inverter circuit 197 having an operational amplifier 198, aninput resistor 199 and a feedback resistor 200. Connected to the outputof the amplifier 198 is a resistor 201 which serves as an input resistorto the amplifier 194. Connected to the output of the amplifier 194 is aseries resistor 202 and a second series resistor 203.

By reference to FIG. 3e, it can be seen that the upper position of theswitch 189 is connected directly to the upper position of the. switch27. The remaining positions are connected in common to the voltagedivider resistors 187,188. Connected to the series resistor 202 is themovable element of a four-position switch 204. The two current positionsof the switch 204 are connected to the input resistor 199 and the twovoltage positions of the switch 204 are connected to the output of theamplifier 194. Also connected to one terminal of the series resistor 203is the movable element of a four-position rotary switch 205 having onlythe lowermost contact point connected directly to the output of theamplifier 194. It can be seen that the switches 189, 204 and 205 aremechanically actuated in common or ganged so that they operate inunison. Furthermore, only the control dial 191 of the switch 189 ismounted on the control panel 5 for common actuation of each of theswitches 189, 204 and 205.

By further reference to FIG. 3e, it can be seen that the amplifier 194and the resistors 195, 196 and 201 form a summer inverter. When theswitch 204 is in either of the two lower positions; that is, the currentpositions, the resistor 202 forms a positive feedback path through theinverter circuit 197 and back to theinverter 193. If the load resistancein the process were of zero magnitude, there would be no positivefeedback loop, and thus the current in the resistor 202 is equivalent tominus the input voltage to the amplifier 194 divided by the value of theresistor 202. If the resistance of the process were of large magnitude,then the positive feedback path through the inverter 197 wouldapproximately equal the negative feedback across the resistor and thiswould cause the output voltage of the amplifier 19410 increase until thesame value of current ,was attained in the resistor 202 that was presentwhen the load was of zero resistance. When the switches 189, 204,

and 205 are unitarily switched to the lowermost position, the resistor203 is placed in parallel with the resistor 202, thus causing morecurrent to flow from the amplifier 194 to the process P for a giveninput voltage. Thus, it can be seen that when the switch 189 and theunitarily actuated switches 204,205 are shifted to either of thelowennost positions, an output current signal is provided independentlyof the process resistance and dependent only on the input voltage signalto the voltage divider consisting of resistors 187,188. When the switch204 is shifted to either of the two upper positions, the seriesresistors 202,203 are effectively removed from the circuit and thepositive feedback loop is also removed permitting the inverter 193 tooperate as a negative feedback inverter. Thus, the output voltage of theinverter 193 is independent of the process resistance and dependent onlyon its input voltage. The switch 189 merely serves to change the scaleof the input voltage-current converter 192 by tapping the dividercircuit consisting of resistors 187,188. This type of range selectorswitching circuit where output voltage and output current is independentof load impedance is more fully illustrated and described in copendingapplication Ser. No. 509,101 filed Nov. 22, 1965.

Thus, it can be seen that the desired input pulse can be manufacturedand transmitted to the process P. The transmission of the pulse to theprocess P will create an output pulse at the selected point ofmeasurement. It should be recognized that the rapid process simulator Ais not necessarily connected to the process either electrically orpneumatically. In many cases, the process is provided with processinstrumentation which may be either pneumatic or electrical or both andthe rapid process simulator A can be connected to the processinstrumentation. However, when reference is made to an operativeconnection between the rapid process simulator A and the process P inthis application, it should be understood that the process P is,therefore, defined to include the process instrumentation associatedtherewith as well as the physical process itself.

As pointed out above, the rapid process simulator A offers utility withmechanical, electrical, biological, chemical systems, etc. In fact, itcan be realized that the rapid process simulator A can be employed withany process as long as conventional conversion components are employedto convert the signal of the process to either pneumatic or electricalsignals as described herein. For example, if a chemical system is to beanalyzed which has pneumatic instrumentation, the E-P transducer 23 andthe P-E transducer 31 are connected to the process. On the other hand,if the process has electrical instrumentation, the connecting lines fromthe electrical and pneumatic range selector are directly connected tothe process at the desired input and output points.

Assuming that the process P was pneumatic and the transducer 32 wasconnected thereto at the desired output signal point, a pneumatic signalfrom the process P would be converted in the P-E converter 31 to anelectrical signal for transmission to the movable arm of a pneumaticrange selector switch 206. The pneumatic range selector switch 206 issubstantially identical to the pneumatic range selector switch 186 andis ganged therewith so that the switch 206 is mechanically actuated bythe switch 186. Therefore, the switch 206 is not mounted on the controlpanel 5. The input signal from the transducer 31 is also transmitted toa pair of series connected input resistors 207,208 of a scale convertersummer 209. By reference to FIG. 3e, it can be seen that the switch 206is connected across the resistor 207 for shorting the same in a mannerhereinafter described in detail. The electrical output from thetransducer 31 will have twice the magnitude on the 630 scale as it doeson the 315 scale. Thus when the resistor 207, which has equal resistancevalue to the resistor 206, is shorted, the gain of the summer 209 isdouble. The summer 209 includes an operational amplifier 210 having afeedback resistor 211.

The model M normally operates on a static voltage level having a zeromagnitude. The process P obviously does not operate on a zero staticlevel and in order to remove the static

1. A pulse generator for producing square and ramp wave pulses, saidgenerator comprising means for receiving a triangular wave input signal,first and second relay comparator circuits operatively connected to saidlast named means for receiving triangular wave signals, firstenergizable means in said first circuit operating a plurality of firstcontacts for producing a square wave, second energizable means in saidsecond circuit operating a plurality of second contacts for producing aramp wave, pulse selecting circuit means operatively connected to eachof said plurality of first and second contacts, and switch means forcausing said selector circuit to function as an inverter circuit toproduce a square wave output and for causing said selector circuit tofunction as an integrator circuit to produce a ramp wave output.
 2. Thepulse generator of claim 1 for producing square and ramp wave pulsesfurther characterized in that potentiometer means is operativelyconnected to each of said relay comparator circuits for adjusting thecommencement time of said pulses and the duration time of each of saidpulses.
 3. A pulse generator for producing square and ramp wave pulses,said generator comprising wave producing means for providing atriangular wave input signal, first and second relay comparator circuitsoperatively connected to said last-named means for receiving triangularwave signals, first energizable means in said first circuit operating aplurality of first contacts for producing a square wave, secondenergizable means in said second circuit operating a plurality of secondcontacts for producing a ramp wave, first pulse selecting circuit meansoperatively connected to each of said plurality of first and secondcontacts, third and fourth relay comparator circuits operativelyconnected to said wave producing means for receiving triangular wavesignals, third energizable means in said third circuit operating aplurality of third contacts for producing a delay square wave, fourthenergizable means in said fourth circuit operating a plurality of fourthcontacts for producing a delay ramp wave, second pulse selecting circuitmeans operatively connected to each of said plurality of third andfourth contacts, and switch means for causing said selector circuits tofunction as inverter circuits to produce a square wave output and forcausing said selector circuits to function as integrator circuits toproduce a ramp wave output.
 4. The pulse generator for producing squareand ramp wave pulses of claim 1 further characterized in that means isprovided for adjusting the transport delay time that said third andfourth selector circuits delay their output signal with respect to saidfirst and second selector circuits.